AOS™ Algebraic Operating System

The AOS™ Algebraic Operating System enables you to enter numbers and combined operations into the calculator in a straightforward sequence. To ensure your calculations are performed in the correct order, the AOS uses algebraic rules to assign priorities to the mathematical operations.

Purpose

WIthout a fixed set of algebraic rules, a problem such as 16-8÷2+6 may have several possible answers, depending on the order in which the operations are completed. However, the Algebraic Operating System solves this problem by completing the division first (8÷2) and then completing the subtraction and addition. Therefore, 16-8÷2+6 = 18.

Pending Operations

In a problem such as 4×5 = 20, simply entering 4 [ × ] 5 does not produce the answer. The operation must be completed by pressing an appropriate key such as [ = ]. (Note that multiplication can be completed by any operation that has equal or lower priority in the algebraic hierarchy.) Until completed, 4 × 5 creates a pending operation.

The RPD-95 Pro can perform calculations containing a maximum of eight pending operations.

NOTE:

Immediate functions, such as x², complete themselves and do not need to be completed by pressing another key.

Algebraic Hierarchy

The AOS algebraic hierarchy completes all operations according to their relative priorities, which are listed below in descending priority.

Immediate Functions - [ SIN ], [ COS ], [ TAN ], [ INV ][ SIN ], [ INV ][ COS ], [ INV ][ TAN ], [ HYP ][ SIN ], [ HYP ][ COS ], [ HYP ][ TAN ], [ INV ][ HYP ][ SIN ], [ INV ][ HYP ][ COS ], [ INV ][ HYP ][ TAN ], [ 2nd ][ nPr ], [ 2nd ][ nCr ], [ 2nd ][ x! ], [ LOG ], [ INV ][ LOG ], [ LN ], [ INV ][ LN ], [ CONV ] functions, [ NUM ] functions, [ x² ], [ √x ], [ 1/x ]
Universal powers and roots - [ yˣ ], [ INV ][ yˣ ]
Multiplications and Division - [ × ], [ ÷ ]
Addition and Subtraction - [ + ], [ - ]
Equals - [ = ]

WIth the AOS hierarchy, lower priority operations are delayed until higher priority operations are complete.

Operations in priority 1 are immediate functions. These functions are performed as soon as you press the keys.
Operations in priority 2, 3, and 4 are completed by any operation with the same or a lower priority. For example, multiplication and division are completed by another [ × ] or [ ÷ ] operation or by [ + ], [ - ], or [ = ].
The [ = ] key completes all operations. If you finish a calculation with the [ = ] key, there is no need to clear the calculator prior to performing another calculation.

Example

The following calculation illustrates the algebraic hierarchy and pending operations.

Calculate 4 + 8 ÷ 2⁵ - 2.

Procedure	Press	Display
Clear display	[ CLEAR ]
Enter addition	4 [ + ]
Enter pending division	8 [ ÷ ]
Enter pending power	2 [ yˣ ]
Complete pending ops, setup subtraction	5 [ - ]
Complete calculation	2 [ = ]